Because the truss is statically determinate, both bars are free to lengthen or shorten, resulting in a displacement of joint B.
Why is being statically determinates related to being free to lengthen or shorten?
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2 Answers
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Because it would otherwise rotate or translate.
Imagine pushing a wall grounded on the wall which is statically determinate (actually its more than that), vs pushing a wall on a trolley. You will be able to move the wall with the same force.
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$\begingroup$ So you're implying that if a truss is statically determinate, then it's also completely constrained. Is that right? $\endgroup$ Commented Jan 28, 2021 at 16:43
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2$\begingroup$ If its statically determinate, it means that it retains its position (completely restarined) with the minimum possible number of constraints. $\endgroup$– NMechCommented Jan 28, 2021 at 16:53
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In an indeterminate truss, the strain and geometry of the members play a significant role. So if we make one shorter or longer the balance of geometry and the distribution of forces will drastically change.
imagine a cantilever beam supported by a prop at the free end. Depending on the length of that prop the cantilever beam can be:
Partially supported
Not supported at all, even being pulled down,
Or the prop is so tall that it not only cancels the loads on the beam but pus the beam under prestress.
But in the truss in your figure, if you increase the length of one of the members, that node moves accordingly, up, down, or to the side. there is no resistance from other members to the movement of the node, they can guide its movement though. of course, if you change the geometry you have to calculate new forces.
